The numbers a , b , and c are positive and a equals 3.2bc . If b is increased by 150% and c is decreased by 60%, then a is
Correct answer: C. unchanged
- A. increased by 90%
- B. increased by 10%
- C. unchanged
- D. decreased by 10%
Explanation
The given equation is a = 3.2bc. We are told that b is increased by 150%, making the new value of b = 2.5b (since 150% of b is 1.5b, adding this to the original b gives 2.5b). Similarly, c is decreased by 60%, making the new value of c = 0.4c (since 60% of c is 0.6c, subtracting this from the original c gives 0.4c).Substituting these new values into the equation for a gives: New a = 3.2 * 2.5b * 0.4c = 3.2bc. This is exactly the same as the original value of a, showing that a is unchanged despite changes in b and c.Therefore, the correct answer is Option C: unchanged. The other options are incorrect as they suggest changes in the value of a that do not occur based on the given percentage adjustments.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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